### Abstract

We use the theory of Witt vectors to develop an algebraic approach for
studying the NTRU primitive with $q$~parameter equal to a power of
two. This results in a system of nonlinear algebraic equations
over~$\FF_2$ having many symmetries, which is reminiscent of the
approach of Courtois, Murphy, Pieprzyk, Robshaw and others for studying
the structure of block ciphers such as the~AES. We study whether
this approach to NTRU provides any immediate security threat and
conclude that under the most favourable assumptions, the method is of
asymptotic interest but is completely impractical at current or likely
future parameter sizes.

Translated title of the contribution | An algebraic approach to NTRU (q = 2^n) via Witt vectors and overdetermined systems of nonlinear equations. |
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Original language | English |

Title of host publication | Security and Cryptography for Networks - SCN 2006 |

Publisher | Springer Berlin Heidelberg |

Pages | 278 - 298 |

Number of pages | 20 |

Volume | 3352 |

ISBN (Print) | 3540243011 |

Publication status | Published - Jan 2005 |

### Bibliographical note

Conference Proceedings/Title of Journal: Security in Communication Networks (SCN 2004)## Fingerprint Dive into the research topics of 'An algebraic approach to NTRU (q = 2^n) via Witt vectors and overdetermined systems of nonlinear equations.'. Together they form a unique fingerprint.

## Cite this

Smart, N., Vercauteren, F., & Silverman, J. (2005). An algebraic approach to NTRU (q = 2^n) via Witt vectors and overdetermined systems of nonlinear equations. In

*Security and Cryptography for Networks - SCN 2006*(Vol. 3352, pp. 278 - 298). Springer Berlin Heidelberg. http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=2000193